Study On Several Kinds Of Polynomial Asymptotic Behavior Based On Evolution Operators

Firstly, this paper reviews the development history of evolution type operators and present situation, we describe some of the current research results briefly.The second chapter is based on the properties of evolution operators, using the theory of functional analysis and operators to discuss the nonuniform polynomial tri-chotomy of evolution operators and its integral characteristic in Banach spaces,so that the concept of uniform polynomial has been generalized to nonuniform polynomial.In chapter 3, for linear discrete-time systems, the definition of nonuniform polyno-mial dichotomy has been given. The main theme of this chapter is the relation between the notion of nonuniform polynomial dichotomy with invariant projection sequences and the notion of Lyapunov function.In chapter 4, we study two nonuniform polynomial trichotomy concepts for lin-ear discrete-time systems in Banach spaces. Our main objective is to give summation property for nonuniform polynomial trichotomies. As for applications we obtain char-acterization of these concepts in terms of Lyapunov functions.In chapter 5, the conclusions and prospects of this paper are summarized.